The maximum compliance constraint can be efficiently handled using the augmented Lagrangian optimization algorithm [1]}. Assume the following maximum compliance constrained problem is to be solved for some objective \(g(\mathbf {x})\)  using the augmented Lagrangian algorithm:
|l|[3]
xg(x)
   Ci = fiT K-1 fi Ct   i 1 ...L
0 xe 1   e 1 ...nE

where \(C_t\)  is the maximum compliance allowed. In the augmented Lagrangian algorithm, the problem is transformed as follows:
|l|[3]
xL(x; , r)
0 xe 1   e 1 ...nE
\(L(\mathbf {x}; \mathbf {\lambda }, r) = g(\mathbf {x}) + \\\sum _{i=1}^{L} \biggl ( \lambda _i (C_i - C_t) + r \max (C_i - C_t, 0)^2 \biggr )\) 
